chlh_jd,
I suggest add the closest point into pointlist , it can reduce a lot of points builded .
Not sure I understand your suggestion. Adding the points you are showing would double the number of points to process, and would be equivalent to to reducing the tolerance.
What I meant, is there are some methods where you generate the point just outside the curve.
This way the tangent cuts the curve at the midpoint of the chord.
Now if you calculate the area of the polyline you will be much closer than with the interpolation method
which is always smaller than true value.
But may be I am missing something in your suggestion.
ymg